Midterm #2 Solutions

Transcription

1 MBA8 EXAM A Spring Mike Conlin February, Midterm # Solutions. ( points) Below is a short article entitled A New Fertility Drug Offers Advantages, But Cost Isn t One Of Them which appeared in the Wall Street Journal. Ares-Serono SA of Switzerland has conceived a fertility drug that is easier to make, more convenient for women to inject and higher in purity and consistency. Similar drugs have been derived from the urine of postmenopausal women, involving complex collection procedures and purification: when orders surged, companies couldn t always produce enough. Serono s new bioengineered drug, Gonal-F, eliminates the use of human urine and ensures an adequate supply. But the price is high and a woman may use two dozen or more per (month). Serono attributes the price to the need to recoup the costs of research and new production facilities. Nonetheless, People will pay whatever it takes to have a baby. It s an emotional issue. says drugindustry analyst Hemant Shah. The graph below depicts the daily demand for Gonal-F. Suppose Serono s total fixed cost is $, and their marginal cost of producing an ampule of Gonal-F is constant at $. (Based on the article, an ampule is the unit of quantity.) D MC MR a) If Serono is profit maximizing, does their statement attributing the high price for Gonal-F to their need to recoup the costs of research make sense? EXPLAIN. Research costs are a fixed cost so they should not influence the price that maximizes profits. b) If Serono cannot price discriminate, what are Serono s daily profits from Gonal-F? SHOW CALCULATIONS. To maximize profits, Serono sets a price equal to $ and sells units. Profits are (-)-=9,.

2 . ( points) The graph below depicts the demand curve and cost curves for a particular Wii Game being sold at Toys R Us in Okemos D MC ATC AVC MR Suppose Toys R Us is currently charging each individual the same price for the game (i.e., Toys R Us does not price discriminate). Toys R Us has the opportunity to hire a consulting firm that would provide them information on their consumers that would enable them to perfectly ( st degree) price discriminate. (Basically the consulting firm would provide Toys R Us with information on what each consumer is willing to pay. Toys R Us can then use this information to perfectly price discrimimate.) Assume that the cost curves depicted on the graph above do not include the fee charged by the consulting firm. Calculate (approximately) the maximum amount Toys R Us should be willing to pay the consulting firm for this information. Let C be the cost of the consultant. Profits if don t pay consultant:.7*7.-7*7.=.9 Profits if pay consultant:.*(-9)*+9*-7*-c=8.-c Maximum willing to pay consultant is C=8.-.9=.8

3 . (9 points) This question is based on my experience when I visited TC Timber. TC Timber is a company located in Skaneateles, New York that manufactures wooden train sets (similar to those produced by Brio). Suppose TC Timber has two types of customers: grandparents and parents. Assume that TC Timber cannot distinguish grandparents from parents. The grandparents are willing to pay a maximum of $ for a wooden train set and parents are willing to pay a maximum of $ for a wooden train set (assuming they do not have to wait in line in order to purchase the train set). There are grandparents and parents. Every year TC Timber has a sale the first weekend in December where they sell the wooden train set for a sale price. Suppose the opportunity cost associated with waiting is $ per hour for grandparents and $ per hour for parents. Assume that TC Timber s marginal cost of a wooden train set is constant at $. Grandparent Parent Maximum Willing to Pay $ $ Opportunity Cost Per Hour $ $ Number a) During this sale weekend, people buying a train set must wait hour in line (there are no lines other than this sale weekend). What price should TC Timber charge for the train set and what should be the sale price? SHOW CALCULATIONS. Let F be TC Timber s total fixed costs. If the parents decide to wait in line and obtain the sale price, the maximum sale price they are willing to pay is $. If the sales price is $, then the maximum TC Timber can set the regular price at so that the grandparents pay the regular price is $ (or you could say $9.99 to make grandparents strictly prefer the regular price to the sale price). TC Timber s profits in this case would be (-)+(-)-F=,-F. If TC Timber did not have a regular price and a sale price and instead had just a regular price, TC Timber s maximum profits would be (-)-F=,-F by setting a price of $. (TC Timber s profits would be (-)-F=,-F if they set a price of.) b) Now suppose the situation is such that TC Timber can choose the number of hours customers wait in line to obtain the sale price. What is this number of hours for customers to wait in line that maximizes TC Timber profits? What are the profits? SHOW CALCULATIONS. It would be hours because that way TC Timber could set a sales price of -= and a regular price of += (the maximum grandparents are willing to pay). Profits would then be (- )+(-)=7,. c) Now suppose the situation is such that TC Timber can not only choose the number of hours customers wait in line to obtain the sale price but also the temperature in the room where the waiting occurs. Suppose TC Timber can select a temperature of F or a temperature of 8 F. At a temperature of F the opportunity cost per hour associated with waiting remains at $ for grandparents and $ for parents. At a temperature of 8 F the opportunity cost per hour associated with waiting is $ for grandparents and $ for parents. (Parents do not mind the higher temperature.) What is the number of hours for customers to wait in line and what temperature is chosen if TC Timber is maximizing profits? What are the profits? SHOW CALCULATIONS. It would be hours at a temperature of 8 F because that way TC Timber could set a sales price of -= and a regular price of += (the maximum grandparents are willing to pay). Profits would then be (-)+(-)=8,.

4 . (8 points) There is demand for a bowling alley from two types of individuals. There are Type A individuals and Type B individuals. Each type s individual demand curve is depicted on the graphs below (where q A is the number of games bowled by a Type A individual and q B is the number of games bowled by a Type B individual). The bowling alley has a constant marginal cost per game of $. and total fixed costs of $. Type A Type B Maximum Type A is willing to pay for shoes Maximum Type B is willing to pay for shoes q A q B Suppose the bowling alley charges $ per game and selects the rental price for bowling shoes so that profits are maximized. (Once an individual pays for the bowling shoes, he/she can wear them to bowl as many games as he/she chooses. An individual cannot bowl at all if he/she does not rent bowling shoes.) What are the bowling alley s profits from this -part pricing scheme if the bowling alley cannot distinguish between Type A and Type B individuals? SHOW ALL CALCULATIONS. If the price per game is $, Type A is going to bowl games and Type B is going to bowl games (assuming the rental price for bowling shoes is not too high). Given the price per game is $, the maximum rental price for bowling shoes that Type A is willing to pay is the red area depicted on the graph. The area equals.*(-)*=8. Using a similar analysis, the maximum rental price for Type B is willing to pay is.*(-)*=.. Profits if shoe rental fee is $8 8*+**-.*(*)-= Profits if shoe rental fee is $..*+**+**-.*(*+*)-= Profits are maximized if the bowling alley charges $8 to rent the bowling shoes.

5 . (7 points) Amazon.com sells two tapes for children under years of age. They are entitled Celebration of Song I and Celebration of Song II. Suppose two types of customers visit Amazon.com: Type A and Type B. There are Type A customers and Type B customers. Type A customers are willing to pay $ for Celebration of Song I and $ for Celebration of Song II. Type B customers are willing to pay $ for Celebration of Song I and $8 for Celebration of Song II. Assume Amazon.com s marginal costs for Celebration of Song I and Celebration of Song II are constant at $ (for each) and Amazon.com has zero fixed costs. Type A () Type B () Marginal Cost Celebration of Song I Celebration of 8 Song II] TOTAL a) Suppose Amazon.com does not bundle. By not bundling, I mean that Amazon.com charges a certain price for Celebration of Song I (p I ) and charges a certain price for Celebration of Song II (p II ). If Amazon.com does not bundle, what prices does Amazon.com select (p I and p II ) and what are their profits? SHOW CALCULATIONS. p I = and p II =8. Profits are (-)+ (8-)= $ b) Now suppose Amazon.com does bundle. By bundling, I mean that Amazon.com charges a single price for both Celebration of Song I and Celebration of Song II (p III ). If Amazon.com does bundle, what price does Amazon.com select and what are their profits? SHOW CALCULATIONS. P I,II =. Profits are (-)= $ c) Now suppose Amazon.com does mixed bundling. If Amazon.com does mixed bundling, what prices are selected and what are Amazon.com profits? SHOW CALCULATIONS. p I,II = and p I =. Profits are (-)+ (-)= $. Or p I,II = and p I =8. Profits are (-)+ (8-)= $. Set p I,II = and p I =.

6 . ( points) Suppose you own a hair salon on Grand River that provides haircuts for women and men. Let the daily demand curves below depict the demand from women (D W ) and the demand for men (D M ). Let the marginal cost of a haircut be the same for a woman as a man and let this marginal cost be constant at $. Assume the daily fixed costs associated with your hair salon are $. Women Men D W D M MR W MR M a) What are your hair salon s maximum daily profits if you third degree price discriminate by charging women a different price than men? Show your calculations. *-*+*-*-= b) Now suppose that it is illegal to directly charge women a different price than men (i.e., illegal to price discriminate based on gender). However, it is legal to offer a coupon that allows the bearer of the coupon to receive a lower price. Assume that the opportunity cost of cutting a coupon is $ for women and the opportunity cost of cutting a coupon is $ for men. To maximize profits, what price would you charge for a haircut and what would be the value of the coupon? What are these profits? Show your calculations and feel free to use the graphs below. (These are the graphs from part a). Women Men D W D M MR W MR M Set Price at $ and coupon value at $. Profits would then be (-)*+(-)*- =. You could then compare these profits with profits if you did not provide a coupon. This was not required.

7 7. ( points) There are two firms (Firm and Firm ) in an industry and the firms produce a homogeneous good. Let Q be the output of Firm and Q be the output of Firm. Let the market demand curve for the good be as depicted below where Q is total output such that Q= Q +Q Q Suppose Firm s marginal cost curve is as depicted below (MC ). D MC Q MR If Firm produces an output of (i.e., Q =), approximately what output should Firm produce in order to maximize his profits? In other words, what is Firm s best response given that Firm produces an output of? EXPLAIN WITH THE ASSISTANCE OF THE ABOVE GRAPH. Firm produces an output of approximately. to maximize profits given that Firm produces an output of.